Compound Interest

Compound interest is a form of interest on a loan or investment that grows over time. The idea of compound interest has been around for thousands of years in various forms. The first part of this series will look solely at the mechanics of compound interest, and later we will look at compound interest in various social and historical contexts. We will define the very basic principles of interest formulas and learn to calculate compound interest using different variables.

To understand what makes compound interest different from other kinds of interest, we will first define simple interest and then take look at a simple interest calculator. With simple interest, the amount of interest applied to a loan is worked out by applying the interest rate. The interest rate is simply a percentage of the initial amount that is to be invested/loaned. For example if the initial amount of a loan was $100 and the interest rate was 5 percent, the amount of interest would be %5.

Therefore the sum total amount including simple interest is the initial amount plus the interest.

However this is just the interest added to the total for one turn. Usually, interest will be added more than once during the lifespan of a loan or investment. If a loan was left unpaid for ten years, then the amount of interest will multiply by ten also. If the interest rate was ten percent, the amount of simple interest added would amount to a doubling of the intitial amount.

Below is a simple interest calculator to find the sum total of a loan/investment that has been incremented using simple interest.

Unlike simple interest, compound interest increases with every turn, whether annually or monthly etc. Compound interest starts off exactly the same as simple interest does, with interest being the percentage of the principal (from now on, we will refer to the initial amount as the principal). What compound interest does is take the first sum total and use that as the new amount from which to apply the second calculation of the interest. If the principal was 100 and the interest rate was 5%, the sum total on the first iteration would be 105. But now we take the interest to be 5% of 105 instead of 100, and apply that interest to the sum total the second go round. Lets apply this concept to our previous examples.

Lets compare the sum totals of simple interest and compound interest over time. You will see that the difference between the two becomes more extreme the more number of times that interest is compounded.

Below is a compound interest calculator to find the sum total of a loan/investment that has been incremented using compound interest annually.

So far we have illustrated what happens when we compound the interest each year at a certain percentage, so over ten years of annually compounding interest, there are ten compounding intervals. However many loans and investments have interests that compound multiple times a year, for example twice or four times a year. This would mean that given a semi-annual compounding interval over ten years, there would be twenty compounding intervals. This would seemingly raise the sum total by an extreme amount, but the the interest rate is also divided by the number of compound intervals in a year meaning the amount of interest added on each compounding interval is smaller. So given an interest rate of 10% and a semi-annual compound interval, the interest rate would be 5 (10/2).

Lets compare the sum totals of simple interest, annually compounding interest, and compounding interest at various intervals over time. The difference between annual compounding and other compounding intervals is not as large as the difference between compounding interest and simple interest. This is because the larger the number of compounding intervals a year, the larger the number that the interest rate is divided by.

Below is a compound interest calculator to find the sum total of a loan/investment that has been incremented at various intervals annually.

Adjusting for inflation is deceptively simple. Take the usual interest rate we have been working with (the Nominal Interest Rate) and subtract it by the inflation rate. This gives you the Real Interest Rate. If the nominal interest rate is 5% and the rate of inflation is 2%, then the real interest rate is 3%.

As just mentioned, this is deceptively simple. You may have noticed that if you set the inflation rate higher than the interest rate you end up with negative figures. This means that an investor can stand to lose purchasing power over the lifespan of an investment. It also means that debtors can use inflation to pay off debts. Real interest is often factored into government borrowing for this reason. Also no one knows what the inflation rate is going to be over time. This brings up lots of questions which will be explored in another article. Below is a compound interest calculator to find the sum total of a loan/investment that has been incremented at various intervals annually, as well as being adjusted for inflation.